%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SEV290^5 : TPTP v8.1.2. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n023.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 19:33:14 EDT 2023

% Result   : Theorem 20.23s 20.46s
% Output   : Proof 20.23s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_c0,type,
    c0: ( $i > $o ) > $o ).

thf(sP1,plain,
    ( sP1
  <=> $false ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: ( ( $i > $o ) > $o ) > $o] :
        ~ ! [X2: ( $i > $o ) > $o] :
            ( ( X1 @ X2 )
           => ! [X3: ( ( $i > $o ) > $o ) > $o] :
                ( ~ ( ( X3 @ X2 )
                   => ~ ! [X4: ( $i > $o ) > $o] :
                          ( ( X3 @ X4 )
                         => ( X3
                            @ ^ [X5: $i > $o] :
                                ~ ! [X6: $i] :
                                    ( ( X5 @ X6 )
                                   => ~ ( X4
                                        @ ^ [X7: $i] :
                                            ~ ( ( X7 != X6 )
                                             => ~ ( X5 @ X7 ) ) ) ) ) ) )
               => ( X3 @ c0 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(def_cSUCC,definition,
    ( cSUCC
    = ( ^ [X1: ( $i > $o ) > $o,X2: $i > $o] :
        ? [X3: $i] :
          ( ( X2 @ X3 )
          & ( X1
            @ ^ [X4: $i] :
                ( ( (~) @ ( X4 = X3 ) )
                & ( X2 @ X4 ) ) ) ) ) ) ).

thf(def_c_less__eq_,definition,
    ( c_less__eq_
    = ( ^ [X1: ( $i > $o ) > $o,X2: ( $i > $o ) > $o] :
        ! [X3: ( ( $i > $o ) > $o ) > $o] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( ( X3 @ X1 )
            & ! [X4: ( $i > $o ) > $o] :
                ( ^ [X5: $o,X6: $o] :
                    ( X5
                   => X6 )
                @ ( X3 @ X4 )
                @ ( X3 @ ( cSUCC @ X4 ) ) ) )
          @ ( X3 @ X2 ) ) ) ) ).

thf(cBLEDSOE1,conjecture,
    ~ sP2 ).

thf(h0,negated_conjecture,
    sP2,
    inference(assume_negation,[status(cth)],[cBLEDSOE1]) ).

thf(1,plain,
    ~ sP1,
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP2
    | sP1 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,h0]) ).

thf(0,theorem,
    ~ sP2,
    inference(contra,[status(thm),contra(discharge,[h0])],[3,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SEV290^5 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.10/0.12  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n023.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Thu Aug 24 02:07:42 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 20.23/20.46  % SZS status Theorem
% 20.23/20.46  % Mode: cade22grackle2x798d
% 20.23/20.46  % Steps: 11
% 20.23/20.46  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------